Well, if we firmly believe the Habsburgs and all their followers were 100% idiots then this ATL will of course go at least as bad as OTL and we will spend a good part of our life filtering out the "evidence" pointing to this - just a question of looking (and overlooking) enough. If we OTOH believe the Habsburgs are nothing short of divine representation here on Earth then any PoD will of course mean the Habsburgs ruling the Universe before Easter!
I think Easter is a bit optimistic

, but as I have before stated that I consider Hungary the biggest problem of the Habsburgs then getting rid of Hungary of course ought to give some opportunities. "Going federal" was on the agenda in late 19th/early 20th century Austria-Hungary, but had no chance with the Hungarians stubbornly blocking anything touching their special role and alongside taking well care of limiting the power of the Kaiser and the army. We of course can't know if such an opportunity would have been utilised but a very big obstacle certainly would have been removed.
Another potential would however have been added and that is of course the loss of prestige involved in loosing a major part of the Empire. In this context I think the future personal role of the Kaisers would be reduced and would be indispensable if some kind of federal constitution is the result of the separation.
The economical core areas of the Empire, Austria and Bohemia, will still be inside the Empire and I guess we will still see the OTL growth in industrialisation - in OTL only second to that in Russia.
As others have already stated life will not necessarily be easy for the new independent Hungary and would offer a splendid opportunity for the Germans and Slavs of the Habsburg Empire to find a common enemy. I guess we could very well see a 2nd Austro-Hungarian War before 1900. In an OTL context we would automatically assume Russia to be allies of the enemies of the Habsburgs, and they might still be, but it will be much more difficult in this ATL because in this ATL it is the Hungarians who are seen as the curse of the Slavs on Balkan.
But Christmas is sure very realistic
...I still haven't said which Christmas
